Most educators will be encountering challenges over the next few weeks and months, as their educational institutions transition to online teaching in response to the novel coronavirus. You probably think teaching math online is particularly problematic and if you asked us five years ago, we would most likely have agreed. In the time since, we’ve taught hundreds of college students math in a real-time virtual classroom at the Minerva Schools. We have learned that it is definitely not trivial, but it is doable, and can even be great. In this article, we aim to share some of our experiences and recommend design decisions to help you transition your math courses to instruction online.
Synchronous (Real-time) Versus Asynchronous Activities
Much of traditional mathematics instruction is still done via lecture-style classes, typically delivered orally and through the use of blackboards. From our experience, this type of instruction translates well to materials that students study asynchronously — typically before a class session. For instance, professors may record videos or share their lecture notes so that students can digest them on their own time ahead of class meetings. To support student engagement with this material, we recommend providing guidance on how to effectively interact with it by embedding quick comprehension checks into the video and including study guides or practice questions in course materials.
In order to reach mastery of mathematical concepts, however, it is vital that students get sufficient practice and exposure to problem-solving. We have seen that problem-solving activities work well in synchronous, collaborative sessions, allowing for efficient face-to-face time with professors, who can give direct feedback. In our class setting, we break students into small groups to work on problem sets directly related to the preparatory material. Synchronous class time is also effective for clarifying any misconceptions and having discussions that connect current and past material.
Creating Asynchronous Materials
As mentioned previously, asynchronous materials for students may include materials that you would produce anyways for a class, such as lecture notes or slides. In the rush to transition your courses online, sticking to what you already have, or finding materials that are readily available might be the most cost-effective strategy. If you are interested and have the time and resources to convert some of these materials for asynchronous student consumption, here are some of the strategies and tips we have developed for our mathematics courses.
Keep it short and digestible
Students may have to get accustomed to pre-class readings, so keeping the materials short and digestible helps ease the transition. This does not necessarily mean that you have to assign less work overall, but you should consider breaking it down into more manageable chunks. For our calculus and linear algebra courses at Minerva, we typically assign two or three ten minute videos to watch along with a study guide that includes one or two comprehension questions and three or four practice problems.
Focus on the goals
When preparing this material, focus on specific goals you have for the session and clearly state those goals to your students. What should be their main takeaways after completing each chunk of the reading? How will they know they have accomplished the goals? The guiding questions for the students should directly address those learning outcomes, which can be explored further during the synchronous class meeting.
Decide on the mode of delivery
We have found that pre-class videos, instead of dense readings, work well with novice learners (first- and second-year students or non-majors.) If you do decide to go this route, we suggest creating the video in stages. First record your screen as you write notes on a digital whiteboard, or annotate a set of slides. We use a writing tablet to draw on the whiteboard, but you may create an annotated set of slides using Beamer (LaTeX slide editor) or even set up your phone to record a video of you writing things down on paper. In either case, we encourage you to include movement in your recordings, which creates a visual anchor for the students as they watch it and helps keep the pace of information flow more reasonable.
After finishing the recording, use a video editing system to do a “voice-over,” narrating your steps. This broken-down approach allows you to fix small mistakes without having to start over. A set of tools, free and paid, that we have used include SketchBook (for drawing, writing equations,) QuickTime (screen recording,) and Camtasia (screen recording, voice narration, and video editing.)
Effective Synchronous Class Strategies
To be blunt, being on a computer connected to the internet is distracting. Due to the way our attentional system has evolved, it is difficult to disregard digital interruptions. (See our colleague Christine Looser’s take on the importance of attention in virtual interactions here.) While students are responsible for actively engaging in their learning, it is our responsibility to design synchronous lessons in a way that motivates students to remain actively engaged during class.
Structuring active synchronous sessions
In our experience, synchronous classes are most effective when students are actively completing well-defined tasks throughout the session. Our goal is to have each student directly engaged for the vast majority of the session. In our experience, students are most engaged when working together in small groups, typically on a problem set. Thus most of our math lessons at Minerva follow the same basic structure:
1. A brief class introduction that outlines specific learning goals for the session (e.g., “This session focuses on linear and quadratic approximations of single variable functions.”).
2. A short-answer poll that is closely related to the readings or material from a previous session. These questions serve as a comprehension check before moving forward. We always ask students to explain their approach when answering. For example, in a calculus course, you might ask, “Find the maximal product of two numbers whose sum is 30. Explain the steps you took to find it.” This poll is followed by a full class debrief that addresses any surfaced confusions. If you do not have the functionality to run free-response polls on your platform, ask students to submit their responses using the chat feature or to a dedicated class email.
3. Next, we send students into small groups (usually two or three students) to work on a problem set collaboratively. There are a few best practices we’ve developed for effective breakouts:
- Be mindful of the difficulty level. Aim for problems that are a step above the preliminary poll. There is no need to reinvent the wheel here. Source problems from examples you might have presented in class or homework problems.
- Provide students with clear expectations for collaboration and communication. Encourage students to discuss problem-solving strategies and derive solutions together rather than splitting the work up among group members. Along with showing their work, ask students to provide an explanation of their approach and justify their reasoning on each problem.
- Student groups work at different paces. Try to plan some flexibility into the task. Have supplemental material for groups that work at a faster pace, or, if you can move participants between groups on your platform, use students who have finished the task as on-the-fly TAs for the other groups.
4. After the breakout session, we typically debrief one or two problems with the entire class. You can involve non-speaking students in the debrief using rapid-fire prompts: Ask students to quickly respond to the current suggestion or solution using a ✓/✗ or give a rating on a three-point scale (e.g., :(, :/, :) ). This could be done with a poll if you have that functionality, using your platform’s chat feature, or even asking students who are on video to hold up one, two, or three fingers. Rapid-fire polls give you a quick method to gauge engagement and spot-check content comprehension before moving on.
5. We conclude classes with a free-response wrap-up poll that both incentivizes students to pay attention throughout the session and prompts them to reflect on their learning for the day. This is usually a novel question closely related to the main skills and concepts from the lesson’s problem set. Like the initial poll, we ask students to outline their process or justify their answers. Simply giving a correct numerical answer is insufficient.
Engaging students during sessions
Once you have a plan in place, you want to think about effectively implementing the plan on your platform.
Aim to keep full-class discussions short, focused, and student-centered. Your job is to be a facilitator, conducting the discussion flow from one student to the next. Use Socratic discussion techniques, quickly moving between students and cold-calling to involve everyone in the conversation. Teach students how to raise their hand by using your classroom tools, or simply by putting their hand up close to the camera. When you call on people, use names — even with everyone on video, eye contact is challenging. Ask students to respond to each other, building on previous suggestions.
When students are in breakout groups, visit them often to check on student engagement and collaboration. Be mindful to engage both students who are active question-askers and those who work quietly.
One of the big lessons we have learned is to “Write things down.” In other words, make sure to have dynamic visual anchors for conversations and discussions. This could be a collaborative document you share with your students (e.g., Google Docs,) writing on an online whiteboard, or live annotating premade slides. This often takes the form of an instructor acting as a “scribe,” while various students explain the next step of a calculation or derivation.
Transitioning to teaching remotely requires you to rethink many aspects of your instruction. It is key to determine which aspects of your course should be asynchronous and which need to be synchronous. There will be challenges but there will also be opportunities. With students scattered across the globe, support them in their desire to stay engaged in their learning and with each other by giving them something active and collaborative to do beyond passively listening, watching, or reading.
Rena Levitt, Lucas Tambasco, and John Levitt are mathematics professors in the College of Computational Sciences at the Minerva Schools where they teach small, active-learning, real-time courses on a virtual classroom called Forum. Before joining Minerva, they taught in brick-and-mortar classrooms at Pomona College, Massachusetts Institute of Technology, and Occidental College.
Looser, C. (2020). Virtual meetings are awful, and it’s probably your fault.